Resonance analysis of a single-walled carbon nanotube

•Resonance behaviors of a single wall carbon nanotubes (SWCNT) with parametric excitation and external excitation is investigated under quasi-periodic perturbation. The global dynamics of the unperturbed system is explored, then the 1:2 subharmonic resonance and 2:1 superharmonic resonance are analyzed using the second averaging method with the assumption that the parametric excitation frequency and external excitation frequency are irrational.•The global dynamics of the unperturbed averaged systems are investigated using Poincare compactification theories. The criteria for the existence of homoclinic Smale chaos of the approximate system with periodic perturbation is obtained by using the homoclinic Melnikov method. To improve the reliability of carbon nanotube sensors is one of the key problems when they are applied to engineering practice. Thus, it is of great theoretical significance and practical engineering application value to study the influence of structural parameters and working environment of micro-nanosensor on the dynamic stability and complex behavior of nonlinear system involved in nanotube devices. In this paper, resonance behaviors of a single wall carbon nanotubes (SWCNT) with parametric excitation and external excitation is investigated under quasi-periodic perturbation. The global dynamics of the unperturbed system is explored, then the 1:2 subharmonic resonance and 2:1 superharmonic resonance are analyzed by using the second averaging method with the assumption that the parametric excitation frequency and external excitation frequency are irrational. Subsequently, the global dynamics of the unperturbed averaged systems are investigated by using Poincaré compactification theories. The criteria for the existence of homoclinic Smale chaos of the approximate system with periodic perturbation is obtained by using the homoclinic Melnikov method. Finally, the numerical simulations including the bifurcation diagrams, Lyapunov exponent spectrums, various orbits (period-1, period-2, chaotic) and Poincaré sections are presented to verify the theoretic results.